If I send a 4K video to my RS45U projector, using cat6 wire with HDMI baluns, will it project at 4K?

The DLA-RS45 upconverts a full HD signal to 4K but does not accept a 4K input.
The projector models that will accept a 4K input signal are the DLA-RS49, DLA-RS4910, DLA-RS57, DLA-RS67, and the DLA-RS6710.